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2 years ago

10

Calculating the give number summary

1 answer:

irga5000 [103]2 years ago

6 0

Answer:

.

Step-by-step explanation:

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Find the general term of sequence defined by these conditions.

disa [49]

Answer:

$\displaystyle a_{n} = (2)^{2n -1} - (3) ^{n-1 }$

Step-by-step explanation:

we want to figure out the general term of the following recurrence relation

$\displaystyle \rm a_{n + 2} - 7a_{n + 1} + 12a_n = 0 \: \: where : \: \:a_1 = 1 \: ,a_2 = 5,$

we are given a linear homogeneous recurrence relation which degree is 2. In order to find the general term ,we need to make it a characteristic equation i.e

${x}^{n} = c_{1} {x}^{n - 1} + c_{2} {x}^{n - 2} + c_{3} {x}^{n -3 } { \dots} + c_{k} {x}^{n - k}$

the steps for solving a linear homogeneous recurrence relation are as follows:

Create the characteristic equation by moving every term to the left-hand side, set equal to zero.
Solve the polynomial by factoring or the quadratic formula.
Determine the form for each solution: distinct roots, repeated roots, or complex roots.
Use initial conditions to find coefficients using systems of equations or matrices.

Step-1:Create the characteristic equation

${x}^{2} - 7x+ 12= 0$

Step-2:Solve the polynomial by factoring

factor the quadratic:

$( {x}^{} - 4)(x - 3) = 0$

solve for x:

$x = \rm 4 \:and \: 3$

Step-3:Determine the form for each solution

since we've two distinct roots,we'd utilize the following formula:

$\displaystyle a_{n} = c_{1} {x} _{1} ^{n } + c_{2} {x} _{2} ^{n }$

so substitute the roots we got:

$\displaystyle a_{n} = c_{1} (4)^{n } + c_{2} (3) ^{n }$

Step-4:Use initial conditions to find coefficients using systems of equations

create the system of equation:

$\begin{cases}\displaystyle 4c_{1} +3 c_{2} = 1 \\ 16c_{1} + 9c_{2} = 5\end{cases}$

solve the system of equation which yields:

$\displaystyle c_{1} = \frac{1}{2} \\ c_{2} = - \frac{1}{3}$

finally substitute:

$\displaystyle a_{n} = \frac{1}{2} (4)^{n } - \frac{1}{3} (3) ^{n }$

$\displaystyle \boxed{ a_{n} = (2)^{2n-1 } - (3) ^{n -1}}$

and we're done!

7 0

3 years ago

S is inversely proportional to t<br> When s = 0.5, t = 7<br> Work out s when t = 0.8

defon

Given:

s is inversely proportional to t.

When s = 0.5, t = 7.

To find:

The value of s when t=0.8.

Solution:

s is inversely proportional to t.

$s\propto \dfrac{1}{t}$

$s=\dfrac{k}{t}$ ...(i)

Where, k is the constant of proportionality.

Putting s=0.5 and t=7, we get

$0.5=\dfrac{k}{7}$

$0.5\times 7=k$

$3.5=k$

Putting k=3.5 in (i), we get

$s=\dfrac{3.5}{t}$

This is the equation of proportionality.

Putting t=0.8, we get

$s=\dfrac{3.5}{0.8}$

$s=4.375
$

Therefore, the value of s is 4.375 when t=0.8.

5 0

2 years ago

If y= -8 when x= -2 whats x when y=32

san4es73 [151]

Answer:

8

Step-by-step explanation:

Y) -8 x -4 = 32

X) -2 x -4 = 8

5 0

3 years ago

Read 2 more answers

At Costco, you can buy a ten-pound bag of Halloween candy for $23.99. Kroger is running a special on the same brand of candy: bu

kirill [66]

Answer:

A. 2.40

B. 4

C. Costco is the better deal

Step-by-step explanation:

23.99/10= 2.399 (rounded to 2.40)

10/2.5 lbs (16 oz = 1 lb) = 4

6 0

3 years ago

I need to round 16,500 nearest thousand feet

Verizon [17]

17,000 feet is your answer

4 0

2 years ago

Read 2 more answers